Strongly unique best coapproximation. (English) Zbl 1086.41013

The notion of best coapproximation, so named by P. L. Papini and I. Singer [Monatsh. Math. 88, 27–44 (1979; Zbl 0421.41017)], was introduced by C. Franchetti and M. Furi [Rev. Roum. Math. Pures Appl. 17, 1045–1048 (1972; Zbl 0245.46024)] to characterize real Hilbert spaces among real reflexive Banach spaces. Subsequently, G. S. Rao has developed this theory. In this paper the authors study strongly unique best coapproximation. Necessary and sufficient conditions characterizing strongly unique best coapproximation and strongly unique best approximation are given. They also study relationships between best uniform approximation and strongly unique best uniform coapproximation.


41A50 Best approximation, Chebyshev systems
41A52 Uniqueness of best approximation
41A99 Approximations and expansions